Sympathetic Vibration vs. String Gauge

All,

Sympathetic vibration being a fact of life for us, has anyone considered the affect of string gauge? Specifically, assuming all other things are equal, will the amount of induced vibration on a "neighbor string" be greater as you increase/decrease relative string gauge? Or lesser...?

Or, is this an irrelevant question since sympathetic vibration is purely dictated by frequency, not string gauge?

Thanks,

A2